Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Savor, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Profits per Rental Class Room Super Saver Deluxe Business Type 1 $40 $35 - (*: Joe says see below) Type 2 $20 $30 $40 Type 1 rooms do not have wireless Internet access and are not available for the Business rental class. Round Tree’s management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type 1 rooms and 120 Type 2 rooms. a. Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Is the demand by any rental type not satisfied? Explain. b. How many reservations can be accommodated in each rental class? c. Management is considering offering a free breakfast to anyone upgrading from a Super Saver reservation to Deluxe class. If the cost of the breakfast to Round Tree is $5, should this incentive be offered? Joe says: Let’s skip part c: it’s a bit tricky to do properly. d. With a little work, an unused office area could be converted to a rental room. If the conversion cost is the same for both types of rooms, would you recommend converting the office to a Type 1 or a Type 2 room? Why?